Year 11 Statistical Investigations AMA Statistics Day 2013 jsaunders@cognition.co.nz

1. Year 11 Statistical InvestigationsAMA Statistics Day 2013jsaunders@cognition.co.nz Pedagogy for improving learning

2. Year 11 Success for all in NCEA Level 1 Statistical Investigations Success for all in statistics may require re-thinking of teacher actions (aka pedagogy). Students need to think flexibly in context and apply both statistical and context knowledge. This workshop will explore teacher pedagogical knowledge for Year 11 students and how it can be adapted to students in other year levels.

3. Effective Pedagogy in Mathematics Glenda Anthony and Margaret Walshaw • Around the room, I have placed the pedagogies recommended by the Best Evidence Synthesis (NZ Ministry of Education). • Please choose one pedagogy and write down the evidence you would expect to see or to hear if that pedagogy was being enacted in the classroom.

4. Ten Principles • An ethic of care • Arranging for learning • Building on students’ thinking • Worthwhile mathematical tasks • Making connections • Assessment for learning • Mathematical communication • Mathematical language • Tools and representations • Teacher knowledge

5. Mrs Saunders, you are teaching us not telling us What is good? • The attention you give us is great. This is a better environment for me to be in rather than a class that’s better at maths than me. • Numbering everyone so that we get a chance to work on the questions. • Making sure everyone is using their initiative. • Teaching methods are engaging and help me understand more. You care about helping us. • Freedom in doing work. • Being able to help each other.

6. Pedagogies to improve learning • Students need to trust their teacher to know them as individuals • As the teacher, I am the authority in the room; from day 1 I begin the journey to convincing them they can learn

7. Teacher as authority The teacher is the expert in the room: • I take the students with me, by articulating a pedagogy and asking them why I use it • I claim my authority in all I say and do I am in charge, so I arrange the seating: • in alphabetical order • seldom changed, and only by me • cycle rows forward from time to time

8. Pause • I wait at least 10 seconds after posing a question before accepting an answer • Why do you think I do this? • Discuss briefly with the person next to you • Tell me what the other person said

9. Re-frame the language • “Miss, is it . . .?” is banned • And give students new language to use (and reiterate it): I think it could be . . . It might be . . . I wonder if it could be . . . • We’re all allowed to make mistakes

10. Ask deeper questions • And give the students opportunities to think before answering • Give out scrap paper to use for working • Encourage each student to think (and write something down) before sharing in a pair

11. My favourite questions: • What can you see? • What is the same and what is different? • How do you know that? • Blog with 26 questions you can ask instead http://mathforum.org/blogs/max/26-questions-you-can-ask-instead/

12. Ask deeper questions • Try to minimise “What is the (one-step) answer” • Aim up the SOLO taxonomy • Ask multi-step questions • Ask for reasons, meaning, applications

13. Every student has to be ready to answer Dylan Wiliam’s method: http://www.dylanwiliam.org/Dylan_Wiliams_website/Welcome.html • Write each student’s name on an ice block stick • Put sticks in a container, randomly pull out a stick to select a student

14. Random numbers • Each student has a number on the roll and they write it down inside exercise book cover • Alphabetical order means . . . • Use this when I want to choose a student to answer – after pausing • I teach one (volunteer) student how to use their calculator to generate a random number from the class • That student always generates random numbers when I want them

15. Do now! • Every lesson starts Do Now Activity hand-written on board • Put up graph, ask for description, possible sources of variation in context, reason for shape in context… • Put up 2 graphs, ask for call and reason for making it, in context • Write a poor paragraph, ask for it to be improved

16. Homework • These students need to learn that doing homework matters • I set a little almost every day • I hold students accountable for doing HW • Students mark their own HW • Open books at start of lesson to show me HW while they complete the Do Now • Students highlight questions they need help with • I record in my mark book whether reasonable attempt or not

17. Feedback • Not just ticks and crosses or N, A, M, E • Always a sentence about what understanding student has shown, and what they need to do to progress • Talk about A and M: What level have we been working on?

18. Dan Meyer suggests • We need to be encouraging patient problem solving and being less helpful. Search for his TED talk: Math Class Needs a Makeover http://blog.mrmeyer.com/ • How can you resist the urge to be helpful?

19. What about NZC Level 6 Statistics? • Start from the beginning of L5, telling a story about the wider universe with supporting evidence.

20. Big Ideas • Data from a sample can be used to answer a question about a population • Data may need to be cleaned – need to know survey questions, who collected from, how collected… • I Census at School!

21. Big Ideas Continued • Inferences should be justified and in context • There are rules we can apply to comparing populations – aka making a call • Reasoning based on shift, overlap, sampling variability and sample size

22. Data Cards Rule • Students physically work with data cards for concept learning • Arrange cards on desks to find median and quartiles, then draw dot plots on provided axes, and draw box plots from the dot plots • Put graphs on wall and use them to develop rules for making calls

23. Getting to Merit and Excellence • Context requires students to • Name the variables • Give values and units • Build up a model for each part of PPDAQ cycle in turn by asking students to just have a go at, say, writing descriptions of graphs • Observe as they write, choose two or three who have good points and work with class to shape them

24. Practice the whole PPDAC cycle • As soon as possible, students should be working on the whole cycle • Plus? Minus? Interesting?

25. Feedback – one facet of an ethic of care • Students should understand where they are aiming • Personal feedback helps them improve • How do you know that? • What is the evidence for your statement? Where is the evidence?

26. Some practice tasks • Practice tasks • Generic questions